半無限域表面承受集中載荷的瞬態解

Transient Solution of Impulsive Loads on Half-Space Surface

利岳聲(Yueh-Sheng Li)

指導教授 ： 葉超雄

國立臺灣大學/工學院/土木工程學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.00276

摘要

颱風，颶風或龍捲風等旋轉風系會造成嚴重災害，大氣學家或氣象學家，著重在其生成原因，這些風系對大地應有影響，即使非常細微，也是值得探討的。
本文即以波動學領域中的半無限域問題分析方法，分析不動颱(颶)風對大地所造成之可能之影響，其一為風壓在無限域表面造成之扭剪效應，另一為氣壓場造成之垂直壓力效應。為接近真實情況，本文特別以Jelesnianski發表的風場及壓力場作為施加的外力，其外力作用場皆涵蓋整個無限域表面，也與過去半無限域問題有所不同。
扭剪效應部份，配合一些假設及前人研究之不動颱(颶)風場，再利用積分表工具書找到部份脈衝型態外力之解析解，不足部份則以Durbin法數值解補足，同時也驗證了解析解的可信度；在此部份，階躍型態外力所造成之半無限域表面效應，也以Durbin法求出數值解。
垂壓效應部份，也以解析解與數值解相互搭配，進而求得脈衝型態外力的半無限域表面反應，並從中發現颱(颶)風對大地並不產生雷利波的效應。其中Mitra無法處理半無限域中核心半徑內區域，也成功地以數值法解決。
本文最終目的，是希望藉由介紹這樣的研究，提供對於旋轉風系力學行為感興趣者與彈性波動學研究者一個跨越兩門科學的方向，進而研究出更多的成果。

關鍵字

颱風 ； 颶風 ； 龍捲風 ； 旋轉風系 ； 半無限域 ； 波動學 ； 扭剪 ； 垂直壓力 ； Durbin

並列摘要

Typhoons, hurricanes or tornadoes, such as cyclostrophic winds can cause serious disasters. Atmospheric scientists, or meteorologists, focus on the reasons for their generation, but in fact these winds should impact the earth and ground. Even if it is very subtle, it is also worthy to explore.
The method of analyzing the half-space problem in the elastic-wave-propagation science is used in this thesis to analyze the possible effects on the earth and ground induced by typhoons or hurricanes. One is thought as the torsional-shear effect induced by the wind stress. Another is the vertical-pressure effect induced by the air pressure of the storms. This thesis features that the wind field and air pressure field studied and published by Jelesnianski are used as the loads in order to simulate the real situation and differs from previous research of the half-space problems because the loads act on whole surface of the half-space.
Regarding the torsonal-shear-effect part, the analytic solutions which don’t cover the whole half-space are found out by using the tool books of integral tables and some hypothesis. The partial solutions are made up by using the Durbin method which has also been used to prove that the analytic solutions are correct. The numerical solutions of the responses on the surface of the half-space induced by the unit-step loads are also obtained by the Durbin method.
The analytic and numerical methods are also collocated to analyze the surface responses of the half-space induced by the impulsive loads within in the vertical-pressure-effect paragraph in which the Rayleigh-wave motion doesn’t appear. The response in the partial area of the half-space that Mitra did not analyze are also solved by the numerical method in this part.
The ultimate goal of this thesis is providing those who want to know more about the mechanical behavior of cyclostrophic winds or elastic waves science researchers with a direction to connect the two kinds of science, then more results may be explored in the future.

並列關鍵字

typhoon ； hurricane ； tornado ； cyclostrophic wind ； half-space ； dynamicelasticity ； torsional ； shear ； vertical pressure ； Durbin

參考文獻

1.Reissner, E. “Freie und erzwungene Torsionschwingungen des elastischen Halbraumes.” Ing.-Arch. Vol.8, 229–245 (1937)

3.Eason, G. “On The Torsional Impulsive Loading of an Elastic Half Space,” Quart. Journ. Mech. and Appl. Math. vol. XVII Pt.3, 279-292 (1964)

4.Ghosh, M. “Displacement Produced in an Elastic Half Space by an Impulsive Torsional Motion of a Circular Ring Source,” PAGEOPH vol.119, No.1, 102-117 (1980/1981)

5.Ghosh, M.& Gosh, M.L. “Torsional Response of an Elastic Half Space to a Nonuniformly Expanding Ring Source,” ZAMM vol.65, 621-629 (1983)

6.Pal, P.C. “On the Disturbance Produced by an Impulsive Torsional Motion of a Circular Ring Source in a Semi-Infinite Transversely Istropic Medium,” Indian J. Pure Appl. Math. Vol.16(2), 179-188 (1985)